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A license plate is made up of three letters and three digits. If repetition is allowed, the letters must come from the set "A, B, C, D, E," and the digits must come from the set "0, 1, 2," how many different license plates are possible?

 

Option: 1

3375


Option: 2

3675


Option: 3

4375


Option: 4

4675


Answers (1)

best_answer

Given that,

The license plate consists of 3 letters and 3 digits.

The first three letters will be from A, B, C, D, and D.

The last three letters will be from 0, 1, and 2.

There are 5 choices for each of the three letters, so the number of different ways to choose the letters is given by,

5 \times 5 \times 5=125

Similarly, there are 3 choices for each of the three digits, so the number of different ways to choose the digits is given by,

3 \times 3 \times 3=27

The number of possible number plates can be calculated using the multiplication principle because the options for the letters and digits are independent.

Thus,

The \, \, total \, \, number \, \, of \, \, possible \, \, license \, \, plates = The \, \, number \, \, of \, \, choices \, \, for\, \, the \, \, letter s \, \, \times \, \, The \, \, number \, \, of \, \, choices \, \, for \, \, the \, \, digits\, \, \\ \begin{aligned}\, \, & N=125 \times 27 \\ & N=3375 \end{aligned}

Therefore, the number of ways to form the license plate is 3375.

Posted by

himanshu.meshram

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